June 18, 2008 Educational Radio Net, PSRG 5th session
Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. Truth be known this subject is a mathematical adventure but, given that we do not have a "white" board for graphic illustration, I will attempt to convey fundamental ideas verbally.
This session is the 4th in the impedance series. Given that impedance is the combination of reactance and resistance and, further, that reactance is an alternating current phenomenon it is clear that we must have some elemental definitions under our belts to fully appreciate the subject. This multi-part series is an attempt to elevate participants, in narrative fashion, to an intuitive level of electrical understanding without using any serious mathematics.
In part 1, I developed the idea of electrical current consisting of moving charge and defined the ampere as 1 coulomb of charge moving past a fixed point in 1 second. One coulomb was defined as a collection of charge numbering 6.24 x 10^18 electrons.
In part 2, I continued with the notion of mechanical "work" and considered objects at different "potential" levels in a gravitational field. The concept of "voltage", also known as electrical potential difference, and the relationship of voltage to current follows closely with the idea of a mechanical weight being moved between different levels. In both cases work is being done and energy is being manipulated in various ways.
In part 3, I capitalized on Bob’s lightning series to review electrical current in the context of a charged cloud redistributing charge in the form of lightning where modest amounts of charge make a large impression if moved rapidly.
In part 4, this edition, I will return to the notion of potential difference and end with a definition of voltage.
Where are we going with these discussions you might ask? Once we have the notions of electrical current and voltage well in hand I will introduce the notion of "power" in both the mechanical and electrical context. After the power discussion I will introduce the physical property of materials called resistance and then merge the voltage, current, and resistance trio into the workhorse notion of Ohm’s Law. Subsequent parts of the series will introduce AC, or alternating current, and DC, or direct current, followed by capacitance and inductance, then reactance, and, finally, I will introduce impedance as the combination of resistance and reactance. All discussion material will be reviewed continually and be available on the blog.
So… let’s take a look at the notion of electrical potential difference. Remember in part 2 we talked about a box on the floor and considered the mechanical work involved in moving the box from the floor to a table top . In this example the Earth’s gravitational field resisted the elevation change of the box. Recall that the box, if falling from the table top to floor, simply gave up the work done when initially moved from floor to table top. Additionally, while on the floor the box had some potential to fall into the basement. So, clearly, one could measure the difference in potential work required in moving between basement and floor and table top. Given that work and energy are identically the same we can make the claim that the energy stored as a result of the box moving from floor to table top is just the difference in potential energy (or work) between these two levels. What are the units of energy? In the physical sciences the common term used is joule. Less common is the erg. Watt-hour meters also measure energy and are commonly found at the electrical entrance to your home. In subsequent parts of this series we will discuss the relationship between energy, power, and time in detail.
You will not be surprised to learn that charge in an electric field behaves much like a box in a gravitational field. Electric fields are produced by charge separation. For example, the lightning associated cloud, or charge separated cloud, in proximity to the Earth’s surface creates a very significant electric field with respect to the Earth's surface. The bottom line is that charge in an electric field gets pushed around. One of the early investigators of these sort of phenomenon was a fellow by the name of Coulomb and the assemblage of charge in the amount of 6.24 x 10^18 electrons bears his name. Coulomb studied the force of attraction or repulsion between two charges and formulated the equation known as Coulomb’s Law which shows the force to be directly related to the charge magnitudes and inversely related to the separation distance squared. Coulomb’s Law is very similar to the universal gravitational law wherein the attraction force is directly related to the objects mass and inversely related to the separation distance squared. In both laws the force drops off very rapidly with separation distance.
Now, let’s consider charge in an electric field. Suppose the field is directed to the right as in points to the right. A positive charge… also know as "conventional" charge… in this field will move in the direction of this field or to the right. If you choose to push the charge in the opposite direction then you must supply energy or, in mechanical terms, do work on the charge to make it move. Now we can define the volt in terms of the work done in moving charge from point A to point B. If you move 1 coulomb of charge in an electric field such that 1 joule of work is done then the potential difference between points A and B is defined as 1 volt. Another way to state this is that 1 joule is required to push 1 coulomb through a potential difference of 1 volt.
Let’s look at the practical ramifications of this definition. Take a D cell for example where common knowledge says that the available voltage is 1.5 volts. Placing both voltmeter probes on the positive terminal shows zero volts or no potential for doing any work. However, placing one probe on the positive terminal and the other on the negative terminal shows 1.5 volt difference and indicates that the battery can do some work. The battery potential difference of 1.5 volts can push some charge through an external circuit and do some useful work. A D cell can do more work than a AA cell since there is more active material available inside the battery to maintain the terminal voltage.
In summary, gravitational fields and electrical fields behave much the same mathematically. In both cases work is done when moving objects against these fields. Relative or "net" work is the difference in potential work at different locations. Net work in the amount of 1 joule is required to move 1 coulomb through a potential difference of 1 volt.
This concludes the set up discussion of electrical potential difference or more simply voltage. Are there any questions related to the concept of voltage?
Showing posts with label work. Show all posts
Showing posts with label work. Show all posts
Tuesday, June 17, 2008
Tuesday, June 10, 2008
IMPEDANCE SERIES PART 2, Lee week 3
June 4, 2008 Educational Radio Net, PSRG 3rd session
One of the topic suggestions from Dave, KE7RJI, was impedance and antenna matching. This is a great topic but one of enormous scope and complexity. After some thought I felt it appropriate to serialize the topic and spread it over several weeks so that we can deal with the component subjects in more detail. To this end we must all speak the same language so a discussion and review of elemental concepts is essential so that we can use them for building blocks. My intent is not to "whip" you into engineers but rather give you the tools to listen to engineers and have a good intuitive understanding of just what is going on.
Impedance is one of the corner stones of electrical theory in general and radio systems in particular. To really grasp the significance of the symbol "Z" requires at least some understanding of the big three circuit elements... resistance, inductance, and capacitance plus some understanding of electrical current and voltage. Last week we started the narrative by discussing the most elemental idea in electrical physics... that of "charge", both moving and stationary. This week we will review "charge" and add the notion of "voltage". In the weeks following we will address the circuit elements in turn and then review and, finally, merge them together into some coherent structure.
Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. Truth be known this subject is a mathematical adventure but, given that we do not have a "white" board for graphic illustration, I will attempt to convey simple ideas verbally.
So, lets get started with the review of "charge".
In the formative years of electrical theory it was understood that something clearly moved when influenced by electrical forces. That hypothetical "something" was given the name "charge" and considered to be positive due to the direction it would move when in the presence of some motive force provided by a, so called, electric field. Modern electrical theory has shown that charge is an electron and, in fact, the elemental electronic charge is negative. So, from a historical perspective, the early and assumed positive charge became known as "conventional" theory in contrast to the now better understood "electron" theory of charge composition.
The electron is very tiny and is normally attached to some atom... helium or hydrogen or some metal such as copper for example. When agitated by forces yet to be discussed the electron can break free of the "mother" atom and become a free electron in contrast to being a "bound" electron before agitation. One free electron bumping along a wire would be impossible to locate or measure without some fancy laboratory instruments however large numbers of moving electrons are readily detected by nanoamp, microamp, milliamp, and just plain ammeters.
There are some very important definitions which are associated with charge.
First. Charge is identically the charge of an electron and is assigned the symbol Q.
Second... the coulomb. This is simply a fixed number of electrons. In fact 1 coulomb is defined as an assemblage of 6.24 x 10^18 electrons and is assigned the symbol C.
Third... the ampere. The ampere is charge in motion and which constitutes electrical current. One "ampere" is defined as 1 coulomb moving past a point in 1 second and enjoys the electrical symbol "I". In the sciences, something per time is known as a "rate" so electrical current... charge in motion... is an example of rate. Other examples are miles/hour, feet/second, apples/minute, coulombs/second, speed, etc.
So, there you have it... a coulomb, with symbol C, is just a known quantity of charge... in a bag for example... and electrical current is just a known quantity of charge moving past a fixed point. A coulomb sitting around doing nothing is electrostatic charge whereas a coulomb marching down a wire is electrodynamic charge and which is the same as electrical current and is measured in amperes.
This concludes the review of charge, moving charge known as electrical current, and the definition of the ampere.
Let's move on to the notion of voltage.
First we need to understand a few things about "work". If you have a box on the floor next to a table and you pick up that box and place on a table then you have done some work. You have moved a box vertically through a gravitational field to do this work. If the box had been in the basement and you moved it to the upstairs table then you would have done more work than just moving it from the upstairs floor to the table. Had you been on the Moon and done the same box moving exercise over the same distances then you would have done less work since the Moon's gravitational field is not as strong as the Earth's. Had you used a lighter box, then you would have done less work on either the Moon or Earth. So, apparently, the amount of work done seems to be related to the "heaviness" of the box, the strength of the gravitational field, and the distance moved.
Now, suppose the box falls from the table to the floor. If you did some work moving the box from floor to table then the box must have also done some work moving from table to floor. In effect the falling box reversed your previous work effort. Apparently the box had some "potential" for doing work while sitting on the table. In like fashion, while sitting on the floor, the box has some potential to fall to the basement. The box actually has the potential to fall to the center of the Earth.
Now we have the ability to define how much work is done in these circumstances. The work you do in moving the box from floor to table is the difference in the two potentials of box on floor and box on table. This is a sneaky way of introducing the notion of potential difference which we can relate directly to voltage potential difference in later segments of this series. Let me just state that "work" and energy are identically the same. We will soon find out that moving electric charge, also known as electrical current, behaves pretty much the same in an electric field as does the moving box in a gravitational field and that voltage is really a measure of electrical potential difference or the ability to do some work.
This concludes the introduction to the concept of voltage. We will develop this voltage notion further and offer a formal definition in the next segment of this series.
One of the topic suggestions from Dave, KE7RJI, was impedance and antenna matching. This is a great topic but one of enormous scope and complexity. After some thought I felt it appropriate to serialize the topic and spread it over several weeks so that we can deal with the component subjects in more detail. To this end we must all speak the same language so a discussion and review of elemental concepts is essential so that we can use them for building blocks. My intent is not to "whip" you into engineers but rather give you the tools to listen to engineers and have a good intuitive understanding of just what is going on.
Impedance is one of the corner stones of electrical theory in general and radio systems in particular. To really grasp the significance of the symbol "Z" requires at least some understanding of the big three circuit elements... resistance, inductance, and capacitance plus some understanding of electrical current and voltage. Last week we started the narrative by discussing the most elemental idea in electrical physics... that of "charge", both moving and stationary. This week we will review "charge" and add the notion of "voltage". In the weeks following we will address the circuit elements in turn and then review and, finally, merge them together into some coherent structure.
Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. Truth be known this subject is a mathematical adventure but, given that we do not have a "white" board for graphic illustration, I will attempt to convey simple ideas verbally.
So, lets get started with the review of "charge".
In the formative years of electrical theory it was understood that something clearly moved when influenced by electrical forces. That hypothetical "something" was given the name "charge" and considered to be positive due to the direction it would move when in the presence of some motive force provided by a, so called, electric field. Modern electrical theory has shown that charge is an electron and, in fact, the elemental electronic charge is negative. So, from a historical perspective, the early and assumed positive charge became known as "conventional" theory in contrast to the now better understood "electron" theory of charge composition.
The electron is very tiny and is normally attached to some atom... helium or hydrogen or some metal such as copper for example. When agitated by forces yet to be discussed the electron can break free of the "mother" atom and become a free electron in contrast to being a "bound" electron before agitation. One free electron bumping along a wire would be impossible to locate or measure without some fancy laboratory instruments however large numbers of moving electrons are readily detected by nanoamp, microamp, milliamp, and just plain ammeters.
There are some very important definitions which are associated with charge.
First. Charge is identically the charge of an electron and is assigned the symbol Q.
Second... the coulomb. This is simply a fixed number of electrons. In fact 1 coulomb is defined as an assemblage of 6.24 x 10^18 electrons and is assigned the symbol C.
Third... the ampere. The ampere is charge in motion and which constitutes electrical current. One "ampere" is defined as 1 coulomb moving past a point in 1 second and enjoys the electrical symbol "I". In the sciences, something per time is known as a "rate" so electrical current... charge in motion... is an example of rate. Other examples are miles/hour, feet/second, apples/minute, coulombs/second, speed, etc.
So, there you have it... a coulomb, with symbol C, is just a known quantity of charge... in a bag for example... and electrical current is just a known quantity of charge moving past a fixed point. A coulomb sitting around doing nothing is electrostatic charge whereas a coulomb marching down a wire is electrodynamic charge and which is the same as electrical current and is measured in amperes.
This concludes the review of charge, moving charge known as electrical current, and the definition of the ampere.
Let's move on to the notion of voltage.
First we need to understand a few things about "work". If you have a box on the floor next to a table and you pick up that box and place on a table then you have done some work. You have moved a box vertically through a gravitational field to do this work. If the box had been in the basement and you moved it to the upstairs table then you would have done more work than just moving it from the upstairs floor to the table. Had you been on the Moon and done the same box moving exercise over the same distances then you would have done less work since the Moon's gravitational field is not as strong as the Earth's. Had you used a lighter box, then you would have done less work on either the Moon or Earth. So, apparently, the amount of work done seems to be related to the "heaviness" of the box, the strength of the gravitational field, and the distance moved.
Now, suppose the box falls from the table to the floor. If you did some work moving the box from floor to table then the box must have also done some work moving from table to floor. In effect the falling box reversed your previous work effort. Apparently the box had some "potential" for doing work while sitting on the table. In like fashion, while sitting on the floor, the box has some potential to fall to the basement. The box actually has the potential to fall to the center of the Earth.
Now we have the ability to define how much work is done in these circumstances. The work you do in moving the box from floor to table is the difference in the two potentials of box on floor and box on table. This is a sneaky way of introducing the notion of potential difference which we can relate directly to voltage potential difference in later segments of this series. Let me just state that "work" and energy are identically the same. We will soon find out that moving electric charge, also known as electrical current, behaves pretty much the same in an electric field as does the moving box in a gravitational field and that voltage is really a measure of electrical potential difference or the ability to do some work.
This concludes the introduction to the concept of voltage. We will develop this voltage notion further and offer a formal definition in the next segment of this series.
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